Fair coins aren’t fair

Many people have flipped coins but few have stopped to ponder the statistical and physical intricacies of the process. In a preregistered study we collected 350,757 coin flips to test the counterintuitive prediction from a physics model of human coin tossing developed by Diaconis, Holmes, and Montgomery (D-H-M; 2007). The model asserts that when people flip an ordinary coin, it tends to land on the same side it started — D-H-M estimated the probability of a same-side outcome to be about 51%. Our data lend strong support to this precise prediction: the coins landed on the same side more often than not, Pr(same side)=0.508, 95% credible interval (CI) [0.506, 0.509], BFsame-side bias=2364. Furthermore, the data revealed considerable between-people variation in the degree of this same-side bias. Our data also confirmed the generic prediction that when people flip an ordinary coin — with the initial side-up randomly determined — it is equally likely to land heads or tails: Pr(heads)=0.500, 95% CI [0.498, 0.502], BFheads-tails bias=0.183. Furthermore, this lack of heads-tails bias does not appear to vary across coins. Our data therefore provide strong evidence that when some (but not all) people flip a fair coin, it tends to land on the same side it started. Our data provide compelling statistical support for D-H-M physics model of coin tossing.

By František Bartoš, et.al., that is a paper from late last year.